Well, I really like this a lot, so I'm going to try me best to tear it apart for you!
1. I think the rocks stick out a little too much, I'd take out the shadows and highlights as you get further from the edge so that it blends into the flat gray better.
2. Why are the hearts for his health quad-pixeled? I think they should be redrawn to fit with everything else. Though perhaps you just grabbed them from somewhere to mock it up.
3. For the animation, he probably shouldn't move back and forth at all, keep the mouth pretty much on a vertical line, and the odd "jumping" will disappear.
4. You could also turn the toes of the feet up on the frame before they hit the ground, it adds a bit more interest and give a little more power to the foot's contact.
5. PypeBros is right about the goggles, while I think it works fine on the idle pose, it looks pretty odd when he's running.
6. His close arm appears to swing back all the way across his back to his far side because you've shaded it with the dark colors on two frames. Actually, I think the biggest problem is that his shoulders don't really move, if you rotate the chest and shoulders to counter the hips and legs it will help a lot.
7. The white spot on his chest moves very erratically, jumping back and forth between frames.
8. I don't think it's good to have the black on the background tree and the forest guardian when the main character is so low-contrast, the black is a little out of place as it is, maybe replace it with another color? Or in the case of the tree, just turn it to transparent.
9. Why is the forest guardian's pose so still? Is he meant to be animated in-engine, with rotateable parts perhaps?
But as I said, I do like this quite a bit! The colors are very nice, and I like the style you've got going, it's very clean and just looks fun to play.